Asset price dynamics in stock-flow consistent macroeco- nomic model M. R. Grasselli Introduction SFC models Goodwin model Keen model Extended Model Conclusions Asset price dynamics in stock-flow consistent macroeconomic model M. R. Grasselli Mathematics and Statistics - McMaster University and Fields Institute for Research in Mathematical Sciences Mathematical Finance Colloquium, University of Southern California, October 06, 2014
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Asset price dynamics in stock-flow consistent ... · Asset price dynamics in stock-flow consistent macroeco-nomic model M. R. Grasselli Introduction SFC models Goodwin model Keen
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Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
Asset price dynamics in stock-flow consistentmacroeconomic model
M. R. Grasselli
Mathematics and Statistics - McMaster University
and Fields Institute for Research in Mathematical Sciences
Mathematical Finance Colloquium, University of SouthernCalifornia, October 06, 2014
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
James Tobin’s contributions to economics
Tobin received the 1981 Nobel Memorial Prize “for hisanalysis of financial markets and their relations toexpenditure decisions, employment, production andprices”.
Well-known contributions included: foundations of modernportfolio theory (with Markowitz), in particular theSeparation Theorem (1958), life-cycle model ofconsumption, Tobit estimator, Tobin’s q, Tobin’s tax, . . .
Key forgotten contribution: financial intermediation,portfolio balances, flow of funds models and the creditchannel.
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
Tobin 1969: A General Equilibrium Approach toMonetary Theory
Specification of (i) a menu of assets, (ii) the factors thatdetermine the demands and supplies of the various assets,and (iii) the manner in which asset prices and interestrates clear these interrelated markets.
Spending decisions are independent from portfoliodecisions.
Each asset i has a rate of return ri and each sector j has anet demand fij for asset i .
Adding up constraint: for each rate of return rk ,
nX
i=1
@fij@rk
= 0.
Paper proceeds to analyze several special cases:money-capital, money-treasuries-capital, banks, etc.
Victim of the Microfoundations Revolution.
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
SMD theorem: something is rotten in GE land
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
Stock-Flow Consistent models
Stock-flow consistent models emerged in the last decadeas a common language for many heterodox schools ofthought in economics.
They consider both real and monetary factorssimultaneously.
Specify the balance sheet and transactions betweensectors.
Accommodate a number of behavioural assumptions in away that is consistent with the underlying accountingstructure.
Reject the RARE individual (representative agent withrational expectations) in favour of SAFE (sectoral averagewith flexible expectations) modelling.
See Godley and Lavoie (2007) for the full framework.
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
Balance Sheets
Balance Sheet HouseholdsFirms
Banks Central Bank Government Sumcurrent capital
Cash +Hh +Hb �H 0
Deposits +Mh +Mf �M 0
Loans �L +L 0
Bills +Bh +Bb +Bc �B 0
Equities +pf Ef + pbEb �pf Ef �pbEb 0
Advances �A +A 0
Capital +pK pK
Inventory +cV cV
Sum (net worth) Xh 0 Xf Xb 0 �B X
Table: Balance sheet in an example of a general SFC model.
No independent specification of consumption (andtherefore savings) for households:
C = W , Sh = 0 (Goodwin)
C = (1� (⇡))Y , Sh = D = ⇧u � I (Keen)
Full capacity utilization.
Everything that is produced is sold.
No active market for equities.
Skott (1989) uses prices as an accommodating variable inthe short run.
Chiarella, Flaschel and Franke (2005) propose a dynamicsfor inventory and expected sales.
Grasselli and Nguyen Huu (2014) provide a synthesis,including equities and Tobin’s portfolio choices.
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Prices
Inventories
Equities
Conclusions
Price dynamics
A general price-wage dynamics taking into account bothlabor costs and expected inflation takes the form
w
w= �(�) + ⌘
1
p
p+ ⌘
2
ie
p
p= �p(c , p) + ⌘
3
ie
d
dt(ie) = ⌘
4
p
p� ie
�,
Here we assume the simplified version
w
w= �(�) + �
p
p,
p
p= �⌘p
1�m
c
p
�
for a constants 0 � 1, ⌘p > 0 and m � 1.
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Prices
Inventories
Equities
Conclusions
Inventory dynamics
Denoting demand by Yd = C + Ik , we postulate thatexpected sales evolve according to
Ye = (↵+ �)Ye + ⌘d(Yd � Ye).
Moreover, we assume that the desired level of inventory isVd = fdYe and that planned changes in inventory aregiven by
Ip = (↵+ �)Vd + ⌘v (Vd � V ).
Finally, production is give by Y = Ye + Ip, which in turndetermines utilization through u = Y /Y
max
= ⌫Y /K .To complete the specification of firm and householdbehaviour we set
Ik =
(⇡e) + ⌘u(u � u)
⌫
�K
pC = c1
W + c2
D
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Prices
Inventories
Equities
Conclusions
Extended System
Defining !p = W /(pY ) and dp = D/(pY ) leads to
!p =!p [�(�)� ↵+ (1� �)⌘p(1�m!p)]
� =� [geye + gdyd � ⌘v � ↵� �]
dp =dp⇥r � geye � gdyd + ⌘v + ⌘p(1�m!p)� c
2
⇤
+ (yd � c1
)!p
ye =ye(↵+ � � ⌘d � geye � gdyd + ⌘v ) + ⌘dyd
u =u [geye + gdyd � ⌘v � yd + c1
!p + c2
dp + �]
,
for constants ge , gd and with
yd = c1
!p + c2
dp +(⇡e) + ⌘u(u � u)
u.
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Prices
Inventories
Equities
Conclusions
Firm decisions
Suppose now that firms finance new investment by issuingequities E at price pe as well as new loans.
Assuming that undistributed profits take the form sf⇧ fora constant sf , the amount needed to be raised externallyfor new investment is pIk � sf⇧, according to theproportions
D = ⌫D [pIk � sf⇧]
pe E = ⌫E [pIk � sf⇧],
with ⌫D + ⌫E = 1.
Here both Ik and ⌫E can be functions of Tobin’s q = peEpK .
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Prices
Inventories
Equities
Conclusions
Household decisions
On the other hand, the budget constraint for households is
W + (1� sf )⇧+ rD = pC + D + pe E ,
whereas their portfolio allocation is
peE = fe(ree )Xh
D = 1� fe(ree )Xh,
where
r ee =(1� sf )⇧
peE+ ⇡e
e
⇡ee = �⇡e
✓pepe
� ⇡ee
◆
This leads to an extended system with two more equationsfor e/e and ⇡e
e .
Asset price
dynamics in
stock-flow
consistent
macroeco-
nomic
model
M. R. Grasselli
Introduction
SFC models
Goodwin
model
Keen model
Extended
Model
Conclusions
Concluding remarks
Macroeconomics is too important to be left tomacroeconomists.
Since Keynes’s death it has developed in two radicallydi↵erent approaches:
1 The dominant one has the appearance of mathematicalrigour (the SMD theorems notwithstanding), but is basedon implausible assumptions, has poor fit to data in general,and is disastrously wrong during crises. Finance plays anegligible role
2 The heterodox approach is grounded in history andinstitutional understanding, takes empirical work muchmore seriously, but is generally averse to mathematics.Finance plays a major role.
It’s clear which approach should be embraced bymathematical finance.